In the literature, when the control domain in nonconvex, it is difficult to derive the first-order and second-order Taylor's expansions for BSDE (REF ), which is proposed as an open problem in Peng [1]}. Recently, Hu [2]} solved this open problem and obtained a novel global maximum principle. In [2]}, the relationship among the terms of the first-order Taylor expansions, i.e.,
\(\begin{aligned}y^1_t&=p_tx^1_t,\\z^1_t&=p_t\delta \sigma (t)\mathbb {I}_{E_{\epsilon }}(t)+[\sigma _x(t)p_t+q_t]x^1_t,\end{aligned}\) 
